You're not alone, most amateurs make that wrong assumption.
Using flash lets you control 2 exposures, ambient light and strobed light, with a single shutter release.
The strobed light can then be used to fill the shadows caused by side and/or back lighting, and the ambient light can be rendered darker than the strobed light so the subject 'pops' (light advances, dark recedes).
That makes sense. So how would you know when to use flash, when photographing in daylight? Or is it a case of experimenting with and without?
Like kundalini indicated professional photographers use supplimental lighting outside a vast majority of the time.
The in-camera light meter can only measure reflected light. Pros use a hand held light meter so they can also measure incident and strobed light at the subject. The meter information tells them
exactly what exposure triad settings to use.
However, a pro will likely adjust those settings in such a way as to produce the same exact exposure, but with different depth-of-field (DOF) and motion stopping capabilities. The changes can be calculated using 5th grade math in your head.
This is where the concept of a photographic stop comes into play.
The following exposure settings will all produce
exactly the same exposure without flash, but with slightly different DOF and motion stopping capabilities:
1/40, f/8, ISO 200
1/40, f/5.6, ISO 100
1/20, F/8, ISO 100
1/80, f/8, ISO 400
1/80, f/5.6, ISO 200
The flash of light from a strobed light source essentially takes over the motion stopping function of shutter speed, because the flash of light has a short duration. A Nikon SB-600 at full power has a flash duration of about 1/900, fast enough to stop the motion of a dog running towards the camera. At 1/2 power the SB-600 flash duration is 1/1600 of a second. Finally at 1/64 power the flash duaration is down to 1/25,000 of a second.
Since shutter speed is no longer needed to stop motion, it can be used to control the ambient light exposure, and we can use the lens aperture to control the strobed light exposure. That is how using strobed lighting allows us to control 2 exposures with a single shutter release.
There are some other considerations like syncing the flash to the front or the rear shutter curtains, and if we have enough flash power available to use flash at shutter speeds above the camera's x-sync speed. X-sync speed is the shutter speed that corresponds to both shutter curtains being fully open. At faster shutter speeds the rear curtain starts closing before the front curtian has fully opened and the flash has to fire multiple time in a rapid sequence to make an exposure that isn't partially blocked by one or both shutter curtains.
Watch this YouTube video:
http://youtu.be/hvZ6VujbhjM